Question: What number could replace $a$ below? $\dfrac{2}{3} = \dfrac{a}{9}$
Answer: The fraction on the left represents 2 out of 3 slices of a rectangular pie. What if we cut the pie into 9 slices instead? How many slices would result in the same amount of pie? We would need 6 slices. $\dfrac{2}{3} = \dfrac{6}{9}$ and so the answer is $6$ Another way to get the answer is to multiply by $\dfrac{3}{3}$ $\dfrac{3}{3} = \dfrac{1}{1} = 1$ so really we are multiplying by 1. The final equation is: $\dfrac{2}{3} \times \dfrac{3}{3} = \dfrac{6}{9} $ so our answer is $6$.